a new method for rapid maximum power point tracking of ... · a new method for rapid maximum power...

Technical Journal of Engineering and Applied Sciences Available online at www.tjeas.com

©2013 TJEAS Journal-2013-3-17/1984-1995

ISSN 2051-0853 ©2013 TJEAS

A New Method for Rapid Maximum Power Point Tracking of PMSG Wind Generator using PSO_

Fuzzy Logic

M. Sarvi1*, Sh. Abdi2, S. Ahmadi3

Faculty of Technical & Engineering, Imam Khomeini International University, Qazvin, Iran

Corresponding author:

M. Sarvi

ABSTRACT: The wind turbine generator is operated such that the rotor speed varies according to wind speed to adjust the duty cycle of power converter and maximizes wind energy conversion system efficiency. The rotating speed of permanent-magnet generator should be adjusted in the real time to capture maximum wind power. This paper proposes a quite simple maximum power point tracking control scheme based on particle swarm optimization_ Fuzzy Logic for wind turbine permanent magnetic synchronous generator system. The system includes the wind-turbine, permanent-magnet generator, three-phase rectifier, boost chopper, load and proposed maximum power point tracking controller. The control parameter is the duty cycle of the chopper. The proposed method is compared with fuzzy logic method. The proposed method has high speed and reliability as well as excellent accuracy to track maximum power point. Also it is robust against distortion (so that power and speed fluctuations are minimized). Keywords: Fuzzy Logic; Maximum Power Point Tracking; Particle Swarm Optimization; Permanent Magnet Synchronous Generator; Wind Power Generation System.

INTRODUCTION

Wind power generation system (WPGS) is one of the most effective power generation systems that convert

the wind energy into some specific forms of electricity. Wind energy has experienced great growth in last year’s. One of the important factors in the development of wind turbines has been the transition from constant speed operation to variable speed (Camblong et al., 2006). The variable speed operation for wind generator is attractive because of its characteristic to achieve maximum efficiency at all wind velocities.

Different types of electric generators are used for the generation of electric energy from wind. These include permanent magnet synchronous generators (PMSG), induction generators, synchronous generators, and doubly fed induction generators. Nowadays, the use of multi polar PMSG represents an important design solution, offering some advantages versus the induction-generator-based configuration, including a simpler and lighter mechanical structure and they do not require any external excitation current (Baroudi et al., 2007; Agarwal et al., 2010; Blaabjerg et al., 2006; Slootweg et al., 2003; Tan and Islam, 2004; Vlad et al., 2010).

To extract maximum energy from wind, an maximum power point tracking (MPPT) control is necessary to adjust the turbine rotor speed according to the variation of wind speeds so that the tip speed-ratio can be maintained at its optimal value (Manwell et al., 2002).

Many methods have been proposed to determine and track the MPPT of the wind, such as the fuzzy logic (Zeng et al., 2008; Hui et al., 2010; Azzouz et al., 2010; Patsios et al., 2009), perturb and observe (Patsios et al., 2009; Koutroulis and Kalaitzakis, 2006), artificial neural network (Ren and Bao, 2010), hill-climbing searching algorithm (Kortabarria et al., 2010) and neuro-fuzzy (Meharrar et al., 2011), gradient approximation algorithm (Hong et al., 2009).

Particle swarm optimization (PSO) algorithm is one of the modern heuristic algorithms. It was developed through simulation of a simplified system, and has been found to be robust in solving continuous nonlinear optimization problems (Zhao et al., 2009). In this paper, a PSO-fuzzy based MPPT is proposed for wind power application. The proposed technique has been applied to a WPGS based on a PMSG operating at variable speed. The performance and accuracy of the proposed method is compared with fuzzy logic algorithm of (Patsios et al., 2009).

Tech J Engin & App Sci., 3 (17): 1984-1995, 2013

1985

This paper is organized as follows: The system configuration is presented in section 2. The proposed MPPT control algorithm is presented in section 3. In section 4, the simulation results are given, analyzed and discussed. Finally, the main conclusions of this paper are presented in section 5.

System Configuration

The studied wind turbine generator system (WTGS) in this paper is shown in Fig. 1. It includes a wind-turbine, PMSG, three-phase bridge rectifier, boost DC/DC converter and a load. The wind turbine converts the power of the wind to mechanical power in the rotor shaft. This is then converted to electrical power using a PMSG. The output voltage is rectified using a three-phase diode bridge rectifier. The dc-to-dc converter is used

to control the dc voltage across capacitor. The duty cycle of the boost DC/DC converter is the only control variable for the achieving MPPT. The resistor provides a virtual load for consuming the real power generation. In the following, each of these subsystems is studied and their models are presented.

Figure 1. Wind turbine generator system

Wind turbine system dynamic model The power extracted from the wind is given in Eq. (1):

3( , )

2m p wind

AP C v

(1)

Where, mP is mechanical output power of the turbine (W ), pC is called the performance coefficient of the

turbine, is air density (3/kg m ), A is the area swept by the rotor blades (

2m ), wind is wind speed ( /m s )

and is blade pitch angle ( deg ). Also tip speed ratio of the rotor blade tip speed to wind speed ( ) is

determined as following:

m

wind

R

(2)

Where, m is the turbine rotational speed expressed ( /rad s ) and R is turbine rotor radius. The mP -

m characteristic of wind turbine is shown in Fig. 2 ( , )pC strongly depends on the wind turbine

aerodynamics and it has been modeled following Eq. (3) (Heier, 2000): 5

21 3 4 6( , ) ( ) i

C

p

i

CC C C C e C

(3)

Where,


1986

2

1 1 0.035

0.8 1i

(4)

The coefficients c1 to c6 are as following: 1 0.5176C , 2 116C , 3 0.4,C 4 55, 21C C and

6 0.0068C . The PC characteristic is shown in Figure 3.

Figure 2. Power characteristic of wind turbine

Figure3. Power coefficient curve

PMSG model In this paper, the wind generator is a three-phase PMSG. The relationship between the rotor angular

velocity of the generator e and the mechanical angular velocity of the rotor m may be expressed as:

2e m

P (5)

The mechanical torque ( mT ) and electrical torque ( eT ) can be expressed as following (Lin and Hong, 2010;

Kesraoui et al., 2010):

mm

m

PT

(6)

2e ee

e m

P PT

P (7)

Where P is the number of PMSG poles. The mechanical system is represented by the following equation:


1987

mm e

dT J T

dt

(8)

Where J is the total inertia which appears on shaft of the wind turbine generator in (2kgm ).The generated

electric power of 3-phase generator is given by:

( ) 3 ( ) ( )e a aP t V t I t (9)

aV and aI are the generator voltage and current, respectively. Assuming no losses in the system, then:

( ) ( ) 3 ( ) ( )m m a aT t t V t I t (10)

Rectifier model A three-phase diode bridge rectifier converts the AC generated output voltage of PMSG, which will be varying in magnitude and also in frequency, into DC. The average output voltage of the three phase diode

rectifier ( dcV ) is obtained as follows (Tan and Islam, 2004):

3 3 mdc

VV

(11)

Where, mV is maximum phase voltage of generated voltage by PMSG.

Boost chopper model The conversion of rectified DC voltage to any specified DC output voltage can be carried out with employing a DC-DC converter or chopper circuit. The boost chopper output voltage is obtained as:

1

1o inV V

D

(12)

Where, D and inV are duty cycle and input voltage of the chopper, respectively, and Vo is chopper output

voltage (Amei et al. 2002).

The Proposed Mppt Control Algorithm Fig. 4 shows the proposed MPPT control block diagram. The MPPT process in the proposed system is based on directly adjusting the DC/DC converter duty cycle according to the measurement of the WG output power and wind speed. Although the wind speed varies highly with time, the power absorbed by the WG varies relatively slowly, because of the slow dynamic response of the interconnected wind-turbine generator system. For variable speed operation, each wind velocity has a maximum power point (Fig. 2). The proposed MPPT flowchart is shown in Fig. 4.

The wind turbine mechanical output power ( mP ) is affected by the ratio of the turbine shaft speed and the wind

velocity, i.e., tip speed ratio ( /m windR v ). As a result of variations in wind velocity, the turbine shaft speed

m (or generator shaft speed) and wind turbine power mP will change.

PSO unit PSO was first introduced by Kennedy and Eberhart in 1995. PSO technique finds the optimal solution using a population of particles. Each particle represents a candidate solution to the problem. PSO is basically developed through simulation of bird flocking in two-dimensional space (Zhao et al., 2009). In the proposed control strategy, the PSO algorithm is used to determine optimum rotor speed of turbine

generator ( m ) and its maximum power ( mP ) according to different wind speeds. The PSO algorithm

parameters used in this paper are presented in Table 1, which determined by trial and error method by using computer simulations.


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Figure 4. The proposed MPPT flowchart

Table 1. Parameters of the PSO Parameter Value

Population size 50 dimension number 1 Maximum iteration 50

maxw 0.9

minw 0.4

1C 2

2C 2

Figure 5. The proposed MPPT control block diagram

Fuzzy logic controller Fuzzy logic control is one of the most powerful control methods where based on fuzzy set theory and associated techniques pioneered by Lotfi Zadeh. Fuzzy logic controller (FLC) is used to adjust boost converter

Start

Measurement of

windv , m and mP

PSO unit

Calculate of mpp and mppP

Calculate of E and E

according to (13) and (14)

Fuzzy-logic controller

Calculate of DC/DC converter duty cycle

Fuzzy-Logic

Controller

Pulse

Generator

Boost Chopper

(DC/DC converter)

PSO

Unit

Calculate

E, ∆E

Unit

D

Pm-optimal

ωm-optimal

Pm-real ωm-real

vwind E

ΔE


1989

duty cycle. According to Fig. 5, FLC is used to accurately adjust duty cycle of DC/DC converter and minimize the error of turbine power. Input parameters of the FLC are error (E) and change of error (ΔE) that are defined as following:

pu pu

m optimal m real

pu pu

m optimal m real

P PE

(13)

( ) ( 1)E E k E k (14)

Where pu

m optimalP and pu

m optimal are per unit optimal values of the speed and power of WTGS in maximum

power point, respectively, where they are obtained from PSO unit and pu

m realP and pu

m real are per unit real time

measured values of the output power and the turbine shaft speed, respectively. FLC output parameter is the duty cycle of the boost converter (D). Seven fuzzy subsets are considered for the membership function of the inputs and output. The values of membership functions are assigned to the linguistic variables using seven fuzzy subsets are called negative big (NB as shown mf1), negative medium (NM as shown mf2), negative small (NS as shown mf3), zero (Z as shown mf4), positive small (PS as shown mf5), positive medium (PM as shown mf6) and positive big (PB as shown mf7). In this paper, error is limited between -1, 1 pu and change of error is limited -0.003, 0.003pu. The rules define the controller behavior by using a set of IF-THEN statements.

The FLC membership functions are shown in Fig. 6. Table 2 represents the control rules where E and E

are inputs and D is the output. After applying the rules, the method of the center of gravity is used for the defuzzication to compute of this FLC which is the duty cycle. The rule surface of FLC is shown in Fig. 7.

(a)

(b)


1990

(C)

Figure 6. FLC membership functions of (a) E; (b) E ; (c) Duty cycle of DC/DC converter

Figure 7. Rule surface of FLC

Figure 8. Pulse generator circuit

Pulse generator unit

The circuit of Fig. 8 is used to generate pulse width according to duty cycle.


1991

SIMULATION RESULTS

In order to investigate the performance and accuracy of the proposed MPPT method, simulations are performed for two models of turbine in MATLAB/SIMULINK facilities. The properties of studied system are presented in Appendix. Also the proposed method is compared with the presented fuzzy logic algorithm in (Patsios et al., 2009).

Figure 9. The diagram of wind speed

Figure 10. The simulated output power ( mP) (MPPT with the proposed algorithm and the presented fuzzy logic controller in

(Patsios et al., 2009)) for step changes in wind speed

Figure 11. The simulated generator shaft speed (MPPT with proposed algorithm and fuzzy logic controller in (Patsios et al.,

2009)) for step changes in wind speed


1992

Figure 12. The simulated performance coefficient of the turbine for step changes in wind speed

Figure 13. The simulated tip speed for step changes in wind speed

Table 3. Comparison of PSO fuzzy and fuzzy logic approaches results in case study.I.

Case study I The system parameters for PMSG and boost converter are presented in the Appendix. To assess the capability of the proposed PSO - fuzzy logic method for MPPT under variation of wind velocity, a step change is applied to the wind velocity. The system is first operating at the wind velocity V = 8m/s. At this velocity, the optimal power is 27.35 kW. At t = 1.5 s, the wind velocity is increased to 9m/s. The optimal power corresponding to this velocity is 38.885 kW. Again, at t = 3 s, the wind velocity is decreased to 7m/s. At this velocity, the optimal power is 18.31 kW. Simulation results for this case study are shown in Figs. 9–13. The simulations are done for the proposed PSO - fuzzy logic method and fuzzy logic method that is presented in (Patsios et al., 2009). Fig. 9 shows the wind speed in the form of fast step variation. The simulated output power, the output rotor speed, performance coefficient of the turbine and tip speed are presented in Figs. 10 - 13, respectively. The simulation results show that the proposed system has high accuracy and reliability in comparison with the presented fuzzy logic method in (Patsios et al. 2009), in tracking of the maximum power point in different wind speeds so that total error remarkably reduces. Table 3 present numerical comparisons between proposed PSO – fuzzy logic approach and presented fuzzy logic approach in (Patsios et al., 2009). According to table 3, it is observed that the proposed approach has higher accuracy in comparison with the presented approach in (Patsios et al., 2009). Case study II The system parameters for PMSG, boost converter and wind turbine are presented in the Appendix. At the first, the system is operating at the wind velocity V = 8m/s. At this velocity, the optimal power is 24.3 kW. At t = 1.5 s, the wind velocity is increased to 9m/s. The optimal power corresponding to this velocity is 33.7 kW.

V=9(m/s) V=8(m/s) V=7(m/s)

Applied Method

Accuracy (%)

m

( /rad s )

mP

( kw )

Accuracy (%)

m

( /rad s )

mP

( kw )

Accuracy (%)

m (

/rad s )

mP

( kw )

100 9.85 38.885 100 8.78 27.35 100 7.66 18.31 Analytical 96.4 10.9 37.5 99.8 9.1 27.3 98.8 8.1 18.1 PSO-Fuzzy 91.3 11.5 35.5 96.8 9.6 26.5 96.6 8.45 17.7 Fuzzy Logic


1993

Again, at t = 3 s, the wind velocity is decreased to 7m/s. At this velocity, the optimal power is 16.3 kW. Simulation results for this case study are shown in Figs. 14-15. The simulations are done for the proposed PSO - fuzzy logic method and fuzzy logic method that presented in (Patsios et al., 2009).

Figure 14. Simulation results of output power ( mP ) (MPPT with the proposed algorithm and the presented fuzzy logic

controller in (Patsios et al., 2009)) for step changes in wind speed (case study II)

Figure 15. Simulation results of generator shaft speed (MPPT with proposed algorithm and fuzzy logic controller in (Patsios

et al., 2009)) for step changes in wind speed (case study II)

Table 4 present numerical comparisons between proposed PSO - fuzzy approach and presented fuzzy logic approach in (Patsios et al., 2009) in case study II. According to Table 4, it is observed that the proposed approach has higher accuracy in comparison with the presented approach in (Patsios et al., 2009).

Table 4. Comparison of PSO fuzzy and fuzzy logic approaches results in case study II

CONCLUSION

In this paper a PSO - fuzzy logic based maximum power point rapid tracking for PMSG wind generator is presented and its characteristics, accuracy and performance is investigated and is compared with the fuzzy logic approach. The analyses and simulations are performed on a system including of a wind-turbine, PMSG, three phase bridge rectifier, boost DC/DC converter and a load. In the proposed control system, the PSO - fuzzy logic controller has been used to track maximum power point of turbine-generator, according to variable wind speed, the PSO optimization algorithm tracks maximum power point and optimizes shaft speed and according to PSO results, the FLC adjust boost converter duty cycle (D). The error between optimized value

V=9(m/s) V=8(m/s) V=7(m/s)

Applied Method

Accuracy (%)

m

( /rad s )

mP

( kw )

Accuracy (%)

m

( /rad s )

mP

( kw )

Accuracy (%)

m (

/rad s )

mP

( kw )

100 8.41 33.7 100 7.47 24.3 100 6.53 16.3 Analytical 93.5 9.75 31.5 96 8.25 23.3 95.6 7.15 15.58 PSO-Fuzzy 86 10.3 28.8 90.1 8.75 21.9 90.2 7.65 14.7 Fuzzy Logic

time (s)

Pm

(W)

time (s)

ωm

(rad

/s)


1994

and measured real value of generator shaft speed and system output power is minimized via FLC too. The proposed MPPT algorithm and the fuzzy logic algorithm evaluated and compared through simulations in MATLAB/SIMULINK. The results of simulations indicate benefits of the proposed MPPT algorithm. The main conclusions of this paper are: High accuracy and speed in tracking maximum power point High reaction against distortions (so that power and speed variations are minimized) High reliability, low cost and complicity Appendix: Characteristics Of The Studied System A – Wind turbine:

Case study I: 21

116( , ) 0.5176( 0.4 5) 0.0068i

p

i

C e

(A.1)

Where,

2

1

1 0.035

0.8 1

i

(A.2)

Case study II:

18.4

2.14151( , ) 0.53( 0.58 0.002 13.2) i

p

i

C e

(A.3)

Where,

3

1

1 0.003

0.02 1

i

(A.4)

The blade radius of the simulated wind turbine is 7.4 m. B - Permanent magnetic synchronous generator PMSG: Number of pole pairs: p = 3;

Stator resistance: sR = 1.6031 F ;

Stator inductance: L = 4.48mH; Flux linkage established by magnets = 5.4782v.s;

Inertia: J = 22.kg m ;

Friction coefficient: F= 51.349*10 N .m .s;

C - Boost DC/DC converter:

Filter capacitance: C = 470 F ;

Filter inductance: L = 17.3mH;

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